Matched filtering techniques for gravitational wave detection. Use when searching for signals in detector data using template waveforms, including both time-domain and frequency-domain approaches. Works with PyCBC for generating templates and performing matched filtering.
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Matched filtering is the primary technique for detecting gravitational wave signals in noisy detector data. It correlates known template waveforms with the detector data to find signals with high signal-to-noise ratio (SNR).
Matched filtering requires:
PyCBC supports both time-domain and frequency-domain approaches.
Generate templates in time domain using get_td_waveform:
from pycbc.waveform import get_td_waveform
from pycbc.filter import matched_filter
# Generate time-domain waveform
hp, hc = get_td_waveform(
approximant='IMRPhenomD', # or 'SEOBNRv4_opt', 'TaylorT4'
mass1=25, # Primary mass (solar masses)
mass2=20, # Secondary mass (solar masses)
delta_t=conditioned.delta_t, # Must match data sampling
f_lower=20 # Lower frequency cutoff (Hz)
)
# Resize template to match data length
hp.resize(len(conditioned))
# Align template: cyclic shift so merger is at the start
template = hp.cyclic_time_shift(hp.start_time)
# Perform matched filtering
snr = matched_filter(
template,
conditioned,
psd=psd,
low_frequency_cutoff=20
)
# Crop edges corrupted by filtering
# Remove 4 seconds for PSD + 4 seconds for template length at start
# Remove 4 seconds at end for PSD
snr = snr.crop(4 + 4, 4)
# Find peak SNR
import numpy as np
peak_idx = np.argmax(abs(snr).numpy())
peak_snr = abs(snr[peak_idx])
Waveforms from get_td_waveform have the merger at time zero. For matched filtering, we typically want the merger aligned at the start of the template. cyclic_time_shift rotates the waveform appropriately.
Generate templates in frequency domain using get_fd_waveform:
from pycbc.waveform import get_fd_waveform
from pycbc.filter import matched_filter
# Calculate frequency resolution
delta_f = 1.0 / conditioned.duration
# Generate frequency-domain waveform
hp, hc = get_fd_waveform(
approximant='IMRPhenomD',
mass1=25,
mass2=20,
delta_f=delta_f, # Frequency resolution (must match data)
f_lower=20 # Lower frequency cutoff (Hz)
)
# Resize template to match PSD length
hp.resize(len(psd))
# Perform matched filtering
snr = matched_filter(
hp,
conditioned,
psd=psd,
low_frequency_cutoff=20
)
# Find peak SNR
import numpy as np
peak_idx = np.argmax(abs(snr).numpy())
peak_snr = abs(snr[peak_idx])
get_td_waveform)get_fd_waveform)Common waveform approximants:
# Phenomenological models (fast, good accuracy)
'IMRPhenomD' # Good for most binary black hole systems
'IMRPhenomPv2' # More accurate for precessing systems
# Effective One-Body models (very accurate, slower)
'SEOBNRv4_opt' # Optimized EOB model (time-domain only typically)
# Post-Newtonian models (approximate, fast)
'TaylorT4' # Post-Newtonian expansion
Note: Some approximants may not be available in frequency domain. If get_fd_waveform fails, use get_td_waveform instead.
low_frequency_cutoffhp.resize(len(conditioned)) - match data lengthhp.resize(len(psd)) - match PSD lengthAfter matched filtering, crop edges corrupted by:
snr.crop(8, 4) for time-domain, snr.crop(4, 4) for frequency-domaindelta_t/delta_f must match dataabs() for SNR: Matched filter returns complex SNR; use magnitudeProblem: "Approximant not available" error
Problem: Template size mismatch
Problem: Poor SNR even with correct masses
Problem: Edge artifacts in SNR time series
pip install pycbc numpy
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